Jó szomszédok a közös jövőért Good neighbours creating common future Dobri susedi zajedno stvaraju budućnost University of Szeged - UNS Faculty of Science Novi Sad Teaching Mathematics and Statistics in Sciences HU-SRB/0901/221/088 Spring School on Mathematics and Computer-Aided Modeling in Sciences Szeged - Novi Sad 2011 organized by University of Szeged and Faculty of Sciences, University of Novi Sad in the frame of the IPA Cross-border Co-operation Programme HU-SRB/0901/221/088 "Teaching Mathematics and Statistics in Sciences: modeling and computer-aided approach" A program a Magyarország – Szerbia IPA Határon Átnyúló Együttműködési Programban az Európai Unió társfinanszírozásával valósul meg. Projekat sufinansira Evropska Unija u sklopu IPA prekogranicnog programa Mađarska-Srbija The project is co-financed by the European Union through Hungary-Serbia IPA cross-border co-operation programme School summary Dates: − Szeged: 05.19.2011 - 05.21.2011 − Novi Sad: 05.27.2011 - 05.29.2011 Groups: − PhD students, researchers (In English) − high school teachers, students (Szeged: in Hungarian, Novi Sad: in Serbian) Audience: We welcome PhD students, researchers, high school teachers and academics from both sides of the border who work in mathematics, physics or other sciences. Talented undergraduate students may also apply with the recommendation of their supervisors. Participating conditions: − Participation is free, participants will receive course materials on DVD. − We have limited possibilities to support accommodation in student hostels. Participants from the other side of the border and participants invited by their results on competitions are of high priority. Travel costs are covered by the participants. − We ask the participants to give seminar at their workplaces or schools for their colleagues and/or students from the subjects they studied on the courses. A report should be prepared from this presentation, illustrated with photographs, which will appear on the website of the project. Information, WWW: − Szeged: www.model.u-szeged.hu − Novi Sad: http://sites.dmi.rs/projects/IPA/ Contact Szeged: − János Karsai PhD, Associate Professor, project manager, [email protected] − Eszter K. Horváth PhD, Assistant Professor, coordinator, [email protected] Novi Sad: − Arpad Takači PhD, Professor, project manager, [email protected] Programme of the schools The courses will concern interesting applications, modeling problems and tools in several areas of sciences in such a way that it will be enjoyable also for non-mathematicians as well. The participants will learn some parts of the following fields: computer-based mathematical applications; computer-aided studies of physical, and biological-chemical models, geometrical structures; digital geography, statistical data analysis; signal processing and computer-aided measuring techniques. For participating teachers, we emphasize the didactic aspects of these techniques. The schools in Szeged and Novi Sad are independent, but they well complement each other. The courses will be held in computer rooms. The participants will study the topics via practical examples. Acreditation: The school is accredited by the Mathematics Doctoral School at University of Szeged (5 credits). It is also accredited as a teachers' training in Serbia. Page: 2 / 23 The programme of the School in Szeged: (May 19-21) Lecturer Course Hours Plenary talks Tibor Krisztin, professor, Bolyai Can we understand the unpredictable? 1 Institute The mathematics of chaos Péter Maróti, professor, Simulation in Biology 1 Department of Med. Physics and Med. Informatics Talks of some prize-winners on the high school competition (2010): 1 Eliza Bánhegyi Then and Now - Triangulation József Attila Gimnázium, Makó Teacher: Erika Rójáné Oláh Andor Viharos Thoughts about the game Maffia Radnóti Miklós Kísérleti Gimnázium, Szeged Teachers: Gábor Ábrahám, Kosztolányiné Erzsébet Nagy, Lajos Pósa, István Tigyi Bernadett Juhász-Bóka Solving quadratic equations by geometric ways Horváth Mihály Gimnázium, Szentes Teacher: Volosin Vlagyimir Annamária Kiss Ramanujan Arany János főgimnázium, Nagyszalonta Teacher: Julianna Mészár Group of researchers and PhD. students (English) Danijela Rajter-Ćirić, professor, On the probability and stochastic models 2 Univ. Novi Sad János Karsai, associate professor Study of dynamic systems with Mathematica 4 Zoltán Kovács, assistant Fractal design with computers 3 professor Ferenc Peták PhD, associate Medical physics practical 4 professor, Dorottya Czövek PhD student Eszter Katonáné Horváth, Islands 2 assistant professor Róbert Vajda, assistant professor Symbolic and numerical study of equations and inequalities 4 with computer algebra software Consultation, workshop 2x1 Total hours: 3+21 Teachers, didactic PhD. students, high school students (Hungarian-English) Đurđica Takači, professor Univ. Mathematical modeling with Pascal triangle (English) 2 Novi Sad Lajos Szilassi, associate professor The camera, what is in front and behind (The specialties of 2 axonometric and perspective visualization) László Égerházi, assistant Medical physics practical 4 professor, Dorottya Czövek PhD student Page: 3 / 23 Krisztina Boda, associate Basic biostatistics with applications 3 professor Géza Makay, associate professor Building a conference center or triangulating surfaces 2 Zoltán Gingl, professor Demonstration experiments with a sound card 2 Péter Makra, assistant professor Attila Máder, assistant professor Computer-aided, exploration centered teaching of math in 2 the practice II. Experimental Mathematics in Action in the Classroom Zoltán Kovács, assistant Free software in mathematics education 2 professor Consultation, workshop 2x1 Total hours: 3+21 The programme of the School in Novi Sad (May 27-29) Lecturer Course Hours Group of researchers and PhD. students (English) Arpad Takači, professor Introduction to Traffic Flow Theory 2 János Karsai, associate Some applications of impulsive systems 2 professor Krisztina Boda, associate Some experiences using multivariate modeling methods en 2 professor, Univ. Szeged paediatric aneasthesia Dušan Mijatović, assist. prof. Mathematica and Anylogic Workshop in Computer laboratory 4 Stevan Pilipović, On the visualizations of generalized functions I 2 academician Marko Nedeljkov, professor Some physical examples 2 Danijela Rajter-Ćirić, On the probability and statistical models 2 professor Đurđica Takači, professor On the visualizations of generalized functions II 2 Branimir Šešelja, professor Fuzzy sets and logic with applications in natural sciences I 2 Andreja Tepavčević, Fuzzy sets and logic with applications in natural sciences II 2 professor Srđan Škrbić, assistant Mathematical background of relational data model 2 professor Total hours 24 Teachers, didactic PhD. students, high school students (Serbian - English) Arpad Takači, PhD, professor Mathematical modeling and simulation in teaching mathematics 2 Géza Makay, associate Sudoku: methods of solutions, how to generate and solve 2 professor, Univ. Szeged, examples with computer; Sudoku competition Attila Máder, assistant Computer-aided, exploration centered teaching of math in the 2 professor, Univ. Szeged practice II. Đurđica Takači, professor On the definition of the logarithmic function, mathematical 4 modeling of earthquake Teodor Atancković, PhD, Introduction to fractional calculus with the applications 2 academician Marko Nedeljkov, PhD, Mathematical models from physics, with the accent on the high 2 professor school contents Duška Pešić, PhD, high Visualization of recursive sequences with Geogebra 2 school teacher Page: 4 / 23 Šešelja Branimir PhD, A generalization of characteristic, fuzzy sets and fuzzy relations, 2 professor their basics properties Andreja Tepavčević, PhD, Applications of fuzzy sets and fuzzy relations in contemporary 2 professor technology (fuzzy controllers in washing machines, video cameras, etc.) Srđan Škrbić, PhD, associate Data basis approach in high school 2 professor Danijela Rajter Ćirić, PhD, Didactical approach of the teaching statistic in high school 2 professor Total hours 24 Summary of the lectures and courses of the school in Szeged Plenary talks Can we understand the unpredictable? The mathematics of chaos Tibor Krisztin DSc., Professor of Mathematics Bolyai Institute, University of Szeged, Hungary The speciality of the chaotic dynamic systems is that the small change of initial data can result in a huge change in the development of the system in the time. Hence, the long time prediction of such systems is impossible. Nevertheless, there are mathematical tools, which can help to measure the phenomenon of the chaos. We show some of them via examples. Simulation in Biology Péter Maróti DSc., Professor of Biophysics Department of Medical Physics and Medical Informatics, University of Szeged, Hungary „If you give me two free parameters, I can describe an elephant. If you give me three, I can make him wiggle his tail.” (Eugene Wigner (1902-1995), Nobel Laureate, Hungarian physicist) The exact description of the biological processes needs a lot of freely chosen parameters. In general, so many that we could make the elephant even to dance. The scientist has the task and responsibility to select the appropriate form of dance. The talk will offer you examples (and unsolved problems) of simulation in two distinct fields of the life sciences. Our aims are to demonstrate how 1) to set up models (to make abstraction), 2) to search for algorithms, 3) to construct elementary computer